If a, b, c, are in A.P, find value of `|a y+4 5y+7 8y+a3y+5 6y+8 9y+b4y+6 7y+9 10 y+c|`

If a,b,c are in A.P find value of |{:(2y+4,5y+7,8y+a),(3y+5,6y+8,9y+b),(4y+6,7y+9,10y+c):}|

If x= 5 and y=2 find the values of : (x^(y)+ y^(x) )

Express the following linear equation in the form of ax+by+c=0 and indicate the values of a, b and c in each case. (i) 8x + 5y - 3 = 0 (ii) 28x - 35y = - 7 (iii) 93x = 12 - 15y (iv) 2x = - 5y (v) x/3+y/4=7 (vi) y=(-3)/2x (vii) 3x+5y=12

Express the following linear equations in the form of ax + by + c = 0 and indicate the values of a, b, c in each case? (i) 3x + 2y = 9 (ii) -2x + 3y = 6 (iii) 9x - 5y = 10 (iv) x/2-y/2-5=0 (v) 2x = y

If a, b, c are in G.P. and a^(1/x) =b^(1/y)=c^(1/z) , prove that x, y , x are in A.P

Express each of the following equations in the form of ax + by + c = 0 and write the values of a, b and c. (i) 3x + 4y = 5 (ii) x - 5 = sqrt3y (iii) 3x = y (iv) x/2+y/2=1/6 (v) 3x - 7 = 0

Find the greatest value of x^3y^4 if 2x + 3y = 7 and x>=0,y>=0 .

If the mean of 6, 7, x, 8, y, 14 is 9,then x + y = . . . .

In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them : (a) 7x + 5y + 6z + 30 = 0 and 3x - y-10z + 4 = 0 (b) 2x + y + 32 - 2 = 0 and x - 2y + 5 = 0 (c) 2x - 2y + 4z + 5 = 0 and 3x - 3y + 6z-1 = 0 (d) 2x – y + 3z-1 = 0 and 2x - y + 3z + 3 = 0 (e) 4x + 8y + z - 8 = 0 and y + z - 4 = 0

Find the area bounded by the lines y= 4x + 5 , y=5 -x and 4y = x +5.